Prince Charles at the Mey Highland Games in John O’Groats, Caithness, earlier this month.
Photograph: Robert MacDonald/PA

Opposition leaders have called on Scottish ministers to publish secret correspondence about lobbying by the Prince of Wales to reform Scotland’s teacher training system.

The Guardian disclosed on Monday that ministers have withheld or redacted documents showing the prince and his officials lobbied them on behalf of a charity called Teach First, of which which he is a patron.

Senior MSPs said there was an overwhelming case for the documents to be released and ministers to make a statement at Holyrood. Iain Gray, Scottish Labour’s education spokesman, said he would be pressing for a parliamentary debate on the disclosures.

“This kind of policymaking under pressure of lobbying, in secret, is no way to embark on ditching a fundamental principle of Scottish education that we only use fully qualified teachers in our schools,” he said.

Teach First, founded in 2002, is interested in bidding for a £1m scheme to train Scottish teachers soon to be launched by Scotland’s government. In England, where the charity has recruited more than 10,000 teachers for state schools and academies, it earns £2,600 per trainee.

Patrick Harvie, the Scottish Green party co-leader, said there needed to be “pretty robust” questioning of ministers about their decision to use a special exemption for the royal family under Scotland’s freedom of information legislation.

Those powers gave the royal family privileges that no commercial lobbying company would be allowed to have, he said, adding that proposals for Holyrood’s committees to investigate Scotland’s information laws should include removing all royal exemptions.

“There’s a serious objection to the idea that an office such as the Prince of Wales’s, which is part of the state, should be used in a way that would fall within regulated lobbying if it was a private company,” Harvie said.

The documents also suggest that the then Scottish first minister Alex Salmond might have discussed Teach First with the Prince of Wales when they met in Edinburgh on 12 June 2013.

A Scottish government briefing from January 2014 refers to a meeting between Salmond and an unnamed Teach First representative, but it has been redacted using the special exemption for members of the royal family. Salmond had not responded to several requests on Tuesday for a comment on the documents.

An unredacted letter from James Westhead, a senior Teach First executive, to a Scottish government civil servant in February 2016 implies that Prince Charles’s private secretary, Mark Leishman, had been briefed by someone inside the Scottish government about its interest in Teach First’s ideas.

Westhead wrote to the Scottish official: “I was in conversation with Mark Leishman last week, who mentioned that there might be interest from your side around the lessons learned by Teach First in England and an exploration of any ideas which might be useful to you in a Scottish context.”

In April 2016, Westhead and another Teach First executive met Scottish officials in Edinburgh. The next month, Nicola Sturgeon, the first minister, wrote to Teach First offering to meet them. She held that meeting in September last year, but it was designated as private and not minuted.

Tavish Scott, the Scottish Liberal Democrats education spokesman, said clarity and openness from the Scottish government was urgently required.

“What Nicola Sturgeon must now do is come clean on what Alex Salmond, her former boss, did and when he did it. Parliament will take a very close interest in this when it returns in a couple of weeks’ time,” he said.

Scottish ministers have previously insisted that the Scottish system allows for more openness about royal correspondence than far stricter legislation in England. They have refused to discuss their reasons for withholding the Teach First papers. Clarence House declined to comment.

The Scottish government refused to comment on the decision to redact and withhold papers on Teach First, but confirmed Salmond met Prince Charles, known as the Duke of Rothesay in Scotland.

A spokeswoman said all such meetings were regarded as private. “The former first minister met the Duke of Rothesay on various occasions in the line of his duties in the role, and their discussions were private, in line with established protocol,” she said.